An Orientation-Sensitive Vassiliev Invariant for Virtual Knots
Geometric Topology
2007-05-23 v3 Combinatorics
Abstract
It is an open question whether there are Vassiliev invariants that can distinguish an oriented knot from its inverse, i.e., the knot with the opposite orientation. In this article, an example is given for a first order Vassiliev invariant that takes different values on a virtual knot and its inverse. The Vassiliev invariant is derived from the Conway polynomial for virtual knots. Furthermore, it is shown that the zeroth order Vassiliev invariant coming from the Conway polynomial cannot distinguish a virtual link from its inverse and that it vanishes for virtual knots.
Keywords
Cite
@article{arxiv.math/0203123,
title = {An Orientation-Sensitive Vassiliev Invariant for Virtual Knots},
author = {J. Sawollek},
journal= {arXiv preprint arXiv:math/0203123},
year = {2007}
}
Comments
13 pages, 10 figures, latex2e, metafont; Corollary 6, Remarks and Example added, several corrections